STEVE AND TORSTEN

We Predict Heights in a few Minutes

Introduction

We collected height data from measurements of floor to nose height, the circumference of an individual’s fist (without the thumb!), and the length of their forearm.

We used markings on the wall and a tape measure to measure people’s heights from the floor to the tip of their nose.

We used a tape measure to measure the length of a person’s forearm, from elbow to the tip of their middle finger.

We used a flexible tape measure to find the circumference of a person’s fist, not including their fist

Floor to Nose Height

It is a very positive, strong, linear model. The correlation coefficient r = .976242.

The residual graph shows no pattern, so a linear model seems to be a good model.

95% of the change in height is explained by change in floor-to-nose height

Floor to Nose Height - Gender

These graphs are also positive, strong and linear, with the male graph being much stronger than the female graph. The male correlation coefficient is .9644 and the female correlation is only .8775.

For males, 93% of the change in height is explained by the change in floor-to-nose height

For females, 77% of the change in height is explained by the change in floor-to-nose height.

Fist Circumference

The graph is positive fairly weak and roughly linear.

The residual plot doesn’t have a pattern and is scattered.

The correlation coefficient of fist circumference to height is .721

52% of the change in height can be explained by the change in fist circumference.

Fist Circumference - Gender

The graphs are positive barely linear and very weak.

The coefficients of males and females, respectively, are .436 and .176

3.1% of the change in height can be explained by the change in fist circumference in females, and 19% of the change in height can be explained by the change in fist circumference in males

Forearm Length

The graph is positive, linear, and fairly strong.

The residual plot has no pattern and fits a linear model.

The correlation coefficient of height and forearm length is .825

68% of the change in height can be exlplained by the change in forearm length

Forearm Length - Gender

Both scatter plots are positive, roughly linear, and moderately weak.

The correlation for males is .5292 and the correlation for females is .5831

28% of the change in height can be explained by the change in forearm length for males

34% of the change in height can be explained by the change in forearm length for females.

Best Model – Nose to Floor!

The floor to nose measurement is the best we have because it is so freakin’ strong. Basically, it IS their height. It is a straight line, almost, and has a very high correlation of .976242. The residual graph is scattered, so the line works well, and all the residuals are relatively low.

Steve’s and Torsten’s Heights

SteveActual Height:

5’ 7.125”Calculated Height:

5’ 5.592”

Residual : 1.534”

TorstenActual Height:

5’ 11”Calculated Height:

5’ 10.934”

Residual: 0.0658”

Heights of Teachers

Height = .994(inches floor to nose) + 6.2Tannous = .994 (61.5) + 6.2Tannous = 67.331” = 5’ 7.331”

Arden = .994 (59.375) + 6.2Arden = 65.219” = 5’ 5.215”

Robinson = .994 (63.375) + 6.2Robinson = 69.195” = 5’ 9.195”

Layton = .994 (63.875) + 6.2Layton = 69.692” = 5’ 9.692”

Walsh = .994 (62.875) + 6.2Walsh = 68.698” = 5’ 8.698”

Bias and Error

We don’t see any real sources of bias. It’s not as if because we knew someone, we gave them an extra inch.

We could, however, have had some errors in measuring. Because it was done in inches, we were more likely to approximate than we would have if we had used centimeters.

Teenage data and adult data are not the same and may have messed with the predictions a bit

Conclusion

Nose to Floor was a successful measurement with highly correlated data. This makes sense because your height to your nose is almost your actual height.

Forearm length was alright as a measurement with a fairly strong correlation. It was easy to measure and efficient, but not our most helpful.

Fist circumference sucked. It was not a big help and was very difficult to measure.